#pragma once
#include "../dfs/info/lib.hpp"
#include "../dfs/top/lib.hpp"
namespace tifa_libs {
template <tree_c G>
struct lca_hld {
using tree_info_t = tree_dfs_info<G, tdi_dfn, tdi_maxson, tdi_dep, tdi_fa>;
tree_info_t info;
vecu top;
CEXP lca_hld(G CR tr) : info{tr} { top = tree_top(tr, info.dfn, info.maxson); }
CEXP u32 operator()(u32 u, u32 v) CNE {
while (top[u] != top[v]) info.dep[top[u]] < info.dep[top[v]] ? v = info.fa[top[v]] : u = info.fa[top[u]];
retif_((info.dep[u] > info.dep[v]), v, u);
}
CEXP ptt<vecptu> getchain(u32 u, u32 v) NE {
u32 lca = (*this)(u, v);
vecptu retu, retv;
while (top[u] != top[lca]) retu.emplace_back(u, top[u]), u = info.fa[top[u]];
retu.emplace_back(u, lca);
while (top[v] != top[lca]) retv.emplace_back(top[v], v), v = info.fa[top[v]];
if (v != lca) retv.emplace_back(info.maxson[lca], v);
reverse(retv);
return {retu, retv};
}
};
} // namespace tifa_libs
#line 2 "src/tree/lca_hld/lib.hpp"
#line 2 "src/tree/dfs/info/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 2 "src/tree/ds/lib.hpp"
#line 2 "src/graph/ds/graph_c/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 4 "src/graph/ds/graph_c/lib.hpp"
namespace tifa_libs {
namespace graph_info_impl_ {
struct graph_info_tag_base {};
template <class... Info>
requires(std::derived_from<Info, graph_info_tag_base> && ...)
struct graph_tag_base : Info... {
CEXP graph_tag_base(auto&&... args) NE : Info(std::forward<decltype(args)>(args)...)... {}
protected:
CEXP void add_arc(auto&&... args) NE { (Info::add_arc(std::forward<decltype(args)>(args)...), ...); }
CEXP void del_arc(auto&&... args) NE { (Info::del_arc(std::forward<decltype(args)>(args)...), ...); }
};
template <class T, class = std::is_void<T>::type>
struct E;
template <class T>
struct E<T, std::false_type> {
u32 to;
T cost;
CEXP E() = default;
CEXP E(u32 v, cT_(T) c) NE : to(v), cost(c) {}
CEXP operator u32() CNE { return to; }
};
template <class T>
struct E<T, std::true_type> {
u32 to;
CEXP E() = default;
CEXP E(u32 v) NE : to(v) {}
CEXP operator u32() CNE { return to; }
};
} // namespace graph_info_impl_
namespace graph_impl_ {
template <class etag_t>
struct graph : etag_t {
using Et = etag_t::val_t;
CEXP graph() = default;
CEXPE graph(u32 n, auto&&... e_args) NE : etag_t(n, std::forward<decltype(e_args)>(e_args)...) {}
CEXP void add_edge(u32 u, u32 v, auto&&... args) NE { etag_t::add_arc(u, v, std::forward<decltype(args)>(args)...), etag_t::add_arc(v, u, std::forward<decltype(args)>(args)...); }
template <class F>
CEXP void foreach(u32 u, F&& f) CNE {
if CEXP (std::is_void_v<Et>)
for (auto v : (*this)[u]) f(v);
else
for (auto [v, w] : (*this)[u]) f(v, w);
}
};
} // namespace graph_impl_
// clang-format off
#define CONCEPT_GRAPH(name, base) \
template <class T> concept name##_c = specialized_from_v<T, base>; \
template <class T> concept u##name##_c = name##_c<T> && std::same_as<TPN T::Et, void>; \
template <class T> concept w##name##_c = name##_c<T> && !std::same_as<TPN T::Et, void>
// clang-format on
CONCEPT_GRAPH(graph, graph_impl_::graph);
} // namespace tifa_libs
#line 4 "src/tree/ds/lib.hpp"
namespace tifa_libs {
template <graph_c graph_t>
struct tree : graph_t {
u32 root;
CEXP tree(graph_t CR g, u32 root = 0) NE : graph_t(g), root(root) {}
CEXP tree(graph_t&& g, u32 root = 0) NE : graph_t(std::move(g)), root(root) {}
CEXPE tree(u32 n, u32 root = 0) NE : graph_t(n), root(root) {}
};
CONCEPT_GRAPH(tree, tree);
} // namespace tifa_libs
#line 5 "src/tree/dfs/info/lib.hpp"
namespace tifa_libs {
struct tdi_dfn {
vecu dfn;
protected:
u32 cnt{0};
CEXPE tdi_dfn(u32 n) NE : dfn(n) {}
void init(u32 u, u32) NE { dfn[u] = cnt++; }
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
struct tdi_sz {
vecu sz;
protected:
CEXPE tdi_sz(u32 n) NE : sz(n) {}
void init(u32 u, u32) NE { sz[u] = 1; }
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32 to, u32 u, auto) NE { sz[u] += sz[to]; }
void before_return(u32, u32) NE {}
};
struct tdi_fa {
vecu fa;
protected:
CEXPE tdi_fa(u32 n) NE : fa(n) {}
void init(u32 u, u32 f) NE { fa[u] = f; }
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
struct tdi_dep {
vecu dep;
protected:
CEXPE tdi_dep(u32 n) NE : dep(n) {}
void init(u32, u32) NE {}
void pre_dfs(u32 to, u32 u, auto) NE { dep[to] = dep[u] + 1; }
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
struct tdi_maxson : tdi_sz {
vecu maxson;
protected:
CEXPE tdi_maxson(u32 n) NE : tdi_sz(n), maxson(n, n) {}
void init(u32 u, u32 f) NE { tdi_sz::init(u, f); }
void pre_dfs(u32 to, u32 u, auto w) NE { tdi_sz::pre_dfs(to, u, w); }
void post_dfs(u32 to, u32 u, auto w) NE {
if (tdi_sz::post_dfs(to, u, w); maxson[u] == (u32)maxson.size() || sz[to] > sz[maxson[u]]) maxson[u] = to;
}
void before_return(u32 u, u32 f) NE { tdi_sz::before_return(u, f); }
};
struct tdi_maxdfn {
vecu maxdfn;
protected:
u32 cnt{0};
CEXPE tdi_maxdfn(u32 n) NE : maxdfn(n) {}
void init(u32, u32) NE { ++cnt; }
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32, u32, auto) NE {}
void before_return(u32 u, u32) NE { maxdfn[u] = cnt - 1; }
};
struct tdi_euler {
vecu euler;
protected:
u32 cnt{0};
CEXPE tdi_euler(u32 n) NE : euler(n) {}
void init(u32 u, u32) NE { euler[cnt++] = u; }
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
struct tdi_go {
vvecu go;
protected:
CEXP static u32 N = 21;
CEXPE tdi_go(u32 n) NE : go(n, vecu(N, n)) { assert(n < 1u << N); }
void init(u32 u, u32 f) NE {
go[u][0] = f;
for (u32 i = 1; i < N && go[u][i - 1] < go.size(); ++i) go[u][i] = go[go[u][i - 1]][i - 1];
}
void pre_dfs(u32, u32, auto) NE {}
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
template <tree_c G>
struct tdi_dis {
using w_t = std::conditional_t<std::is_void_v<TPN G::Et>, u32, TPN G::Et>;
vec<w_t> dis;
protected:
CEXPE tdi_dis(u32 n) NE : dis(n) {}
void init(u32, u32) NE {}
void pre_dfs(u32 to, u32 u, auto w) NE { dis[to] = dis[u] + w; }
void post_dfs(u32, u32, auto) NE {}
void before_return(u32, u32) NE {}
};
template <tree_c G, class... Ts>
struct tree_dfs_info : Ts... {
using w_t = std::conditional_t<std::is_void_v<TPN G::Et>, u32, TPN G::Et>;
CEXPE tree_dfs_info(G CR tree) : Ts(tree.vsize())... { dfs(tree, tree.root); }
private:
void dfs(G CR g, u32 u, u32 fa = -1_u32) NE {
if CEXP ((Ts::init(u, fa), ...); wtree_c<G>) {
for (auto [v, w] : g[u])
if (v != fa) (Ts::pre_dfs(v, u, w), ...), dfs(g, v, u), (Ts::post_dfs(v, u, w), ...);
} else
for (auto v : g[u])
if ((u32)v != fa) (Ts::pre_dfs((u32)v, u, 1), ...), dfs(g, (u32)v, u), (Ts::post_dfs((u32)v, u, 1), ...);
(Ts::before_return(u, fa), ...);
}
};
} // namespace tifa_libs
#line 2 "src/tree/dfs/top/lib.hpp"
#line 5 "src/tree/dfs/top/lib.hpp"
namespace tifa_libs {
template <tree_c G, bool need_dfn = false>
CEXP vecu tree_top(G CR tr, std::conditional_t<need_dfn, vecu&, spnu> dfn, spnu maxson) NE {
cu32 n = tr.vsize();
if CEXP (need_dfn) dfn = vecu(n);
vecu top(n, n);
u32 cnt = 0; // NOLINT(misc-const-correctness)
auto f = [&](auto&& f, u32 u, u32 top_) NE -> void {
if CEXP (need_dfn) dfn[u] = cnt++;
if (top[u] = top_; maxson[u] == tr.vsize()) return;
for (f(f, maxson[u], top_); auto v : tr[u])
if (top[(u32)v] == tr.vsize()) f(f, (u32)v, (u32)v);
};
f(f, tr.root, tr.root);
return top;
}
} // namespace tifa_libs
#line 5 "src/tree/lca_hld/lib.hpp"
namespace tifa_libs {
template <tree_c G>
struct lca_hld {
using tree_info_t = tree_dfs_info<G, tdi_dfn, tdi_maxson, tdi_dep, tdi_fa>;
tree_info_t info;
vecu top;
CEXP lca_hld(G CR tr) : info{tr} { top = tree_top(tr, info.dfn, info.maxson); }
CEXP u32 operator()(u32 u, u32 v) CNE {
while (top[u] != top[v]) info.dep[top[u]] < info.dep[top[v]] ? v = info.fa[top[v]] : u = info.fa[top[u]];
retif_((info.dep[u] > info.dep[v]), v, u);
}
CEXP ptt<vecptu> getchain(u32 u, u32 v) NE {
u32 lca = (*this)(u, v);
vecptu retu, retv;
while (top[u] != top[lca]) retu.emplace_back(u, top[u]), u = info.fa[top[u]];
retu.emplace_back(u, lca);
while (top[v] != top[lca]) retv.emplace_back(top[v], v), v = info.fa[top[v]];
if (v != lca) retv.emplace_back(info.maxson[lca], v);
reverse(retv);
return {retu, retv};
}
};
} // namespace tifa_libs
src/tree/lca_hld/lib.hpp